Rho,
In terms of if the cost is being passed on to the taxpayer, yes of course it is. The taxpayer is footing the bill for the whole shooting match, not just the type ratings. The wise SAR Team at BRS have no doubt costed this well, check the quarterly filing from last week, BRS claim they are doing very well indeed out of UK SAR. (Imagine how bad their results would be without it!)...
Jim raises an interesting perspective about HMG involvement in the ac types. With the withdrawal of the WAH64 and replacement with genuine Boeing AH64 in the future for the Army, AW/ Leonardo have effectively been significantly downsized in HMG Military procurement in the UK (Wildcat and derivatives and Merlin left). I'd expect HMG to throw them a bone somewhere in future ac purchasing requirements if they can in order to keep the factory open. Quite which ac need replacing with Leonardo products I have no idea.